$1CNF$ and DNF Formulas

In the case of the following formulas point out whether they are CNF or DNF formula writing $"$CNF$"$ or $"$DNF$"$ if

necessary:

$[(pvvnotq{)}^{{?}^{?}}(notpvvnotqvvr)]vv(not{p}^{{?}^{?}}r)$

$not{p}^{{?}^{?}}{q}^{{?}^{?}}$notr

$*$ pvvnotnotq

notq

not$(notpvvq)vvnotr$

$(notpvvnotq{)}^{{?}^{?}}r$

$(p^{{?}^{?}}$notq$)vvnotr$

$2CNF$

Transform to CNF $($conjunction normal form$)$ the following formula:

$(notA)>(AvvB)$

$3$ DNF

Transform to DNF $($disjunction normal form$)$ the following formula:

$(notA)>(AvvB)$

$4$ Resolution

Using resolution show unsatisfiability of the following set of clauses:

$S=\{p,$notpvvq,$qvvs,rvvs,$rvvnots,notrvvt,notrvvnott,pvvnotp$\}.$

$5CNF$ and Resolution

Transform to CNF and using resolution show that hawing in knowledge base the following facts $(p=>$notz$)$ and $q$ one

can deduce that $(q=>z)=>p.$

$6$ Saturated and Unsaturated Formulas

In the case of following formulas decide whether they are saturated or unsaturated formula writing $"S",$ if the formula

is saturated or "UNS", if the formula is unsaturated:

$[P(x,a)vvR(x,y){]}^{{?}^{?}}$notQ$(z)$

$R(a,f(a){)}^{{?}^{?}}Q(z)$

$R(a,b{)}^{{?}^{?}}P(a,c{)}^{{?}^{?}}Q(b)$

$P(a,f(x))vvnotR(a,c)vvQ(b)$

notP$(a,c{)}^{{?}^{?}}R(b,f(b){)}^{{?}^{?}}$notQ$(a)$

where $P,R$ are predicates, $f$ is a functional symbol, $x,y,z$ are individual variables and $a,b$ are constants.